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Dr Gian Domenico Iannetti, one of the researchers behind the study at the department of neuroscience at University College London, said the distance appeared to be a defensive mechanism employed by the brain.

He said their findings could be useful for helping assess how police and other emergency service personnel respond to stressful situations. It could also help them assess threats more accurately.

He said: “These findings indicate that the defensive peri-personal space has a clear boundary.

"This space is very much related to defence – the point where we start to feel threatened. It is linked to social personal space but it is not the same.

"We think the defensive space is something that we constantly update depending on the context. These measures we obtained were in a friendly lab environment.

"If you are chatting to someone in your living room, you won't have a large safety margin at all, but if you are walking through a dangerous area then that will be much bigger.

"In places like the tube, it is not a threatening situation, so we are probably more accepting of being that close to people. It can be annoying but not threatening."

Invasion of personal space has become a growing problem on Britain’s overcrowded train and public transport networks.

Most people have a limit where they will feel uncomfortable but the latest research measures the point at which people start to feel threatened.

It is thought to be a cultural issue, however, as in other countries such as China and India, personal space is seen as being less important.

Dr Iannetti said he hoped to carry out research on subjects from other countries to better understand differences between cultures.

In the current research, which is published in the Journal of Neuroscience, 15 volunteers aged between 20 and 37 had their peripersonal space assessed.

The researchers got the volunteers to hold their hands different distances from their face before giving them a strong electric shock on their hand.

They assessed their reaction to the shock, which did not change in intensity, by measuring the amount the volunteers blinked.

The more they blinked the more of a threat they felt the shock was to their face. The subjects were also asked to complete anxiety tests.

Dr Iannetti and his colleagues found that rather than having a gradual increase, the personal space of the volunteers appeared to have an abrupt boundary where they felt threatened.

This varied according to individuals but it was generally around eight to 16 inches from their face.

Those who were rated as being more anxious were more sensitive and had larger defensive personal spaces.

Dr Iannetti said: "This finding is the first objective measure of the size of the area surrounding the face that each individual considers at high-risk, and thus wants to protect through the most effective defensive motor responses."

Debrett's, which publishes guides to manners and etiquette, offers extensive advice to those who feel their personal space is being invaded.

It says that if you are close enough to feel the warmth of someone's breath on your face then you are too close together.

They say that rather than trying to back away, it is better to create more space by turning to wave at someone passing, or turning to get something out of a bag.

They state: "It is an undeniable fact that some people always stand too close. Even on crowded public transport, there is inescapably close and threateningly close.

"When someone steps over that invisible line, when you start to feel troubled, you want to step backwards away from the space-invader.

"The trick here is not to back away but to somehow create a whole new space."